Chart of the Day: US Median Floor Area Per Capita Trends

Here is an elegant and revealing chart from Douglas Farr’s new textbook, “Sustainable Nation.” It comes from Chapter One, “Where We Are” and shows the growth in housing space per person over the last fifty or so years:

Note that this data is for the United States, and is taken from US census data cited in the text. The people in the corner show the average US household size, and the two shades are for housing type.

Farr pairs the chart with a happiness ranking, showing that the US is only 13th in the world for global happiness, despite our increasingly large homes.

From the Census Bureau: “Number of Housing Units in Structure. A structure is a separate building which either has open space on all four sides or is separated from other structures by dividing walls that extend from ground to roof. In double houses, row houses, and houses attached to nonresidential structures, each building is a structure if the common wall between them goes from ground to roof. Sheds and private garages which adjoin houses are not counted as separate structures. In apartment developments, each building with open space on all sides is considered a separate structure. The count of housing units in a structure is the total number of units in the structure, both occupied and vacant units. In the tabulations, occupied mobile homes or trailers, tents, and boats are included in the category one housing unit in structure.”

It may be elegant, but it is so horribly misleading in many regards that it can’t possibly be revealing.

(1) The areas of the boxes are not to scale. The largest box, labeled 926′, and the smallest, labeled 296′, ought to be in a ratio of a bit over 3:1. Given that these numbers are areas (in square feet, not linear feet despite the symbol), that ratio ought to be the ratio of areas. But in fact the largest box appears to be about 3 times as wide and 3 times as tall as the smallest box, producing an area ratio of roughly 9:1 instead of 3:1.

(2) The average household sizes are wrong. You shouldn’t need to look at census numbers to know that in 1973, the average household did not have 6 members. (The actual number is 3.01.) One might think the idea was a more abstract display of household size in which rather than counting the people in the group, one sees how wide in millimeters it is.(Because the heights are consistent, there’s no difference between ratio of width and ratio of area for the group of silhouettes, unlike with the boxes.) However, that doesn’t work out either. The 1973 average household size was only 3.01/2.54=1.19 times as large as the 2014 average, whereas the group on the left is twice as large as the one on the right in size as well as in count.

(3) Scaling the boxes to *per capita* area (assuming that had been done correctly) and then putting variable numbers of people inside them is incoherent. Every box should have exactly one person, since they are per capita. By putting variable numbers of people inside (assuming that had been done correctly), the author was double counting the change in household size and making the 1973 household look even more crowded compared to 2014 than is the reality. If the goal were to show a typical household, then the size of the box shouldn’t be per capita, it should be for the whole household. (For example, in 1973, the median single-family home in the US had an area of 1,525 square feet.)

(4) Without checking the book I can’t be sure, but it seems the calculation of median area per capita was done incorrectly. These numbers look like what you would get if you divide the media area per household by the average household size. That can give a different answer from what you’d get if for each household you divided the area by the number of people, getting an area per capita for that household, and then took the median of those. It’s hard for me to know a priori whether this makes a significant difference, unlike the first three points that definitely do. (Also, using a single average household size for both single-family and multi-family housing units doesn’t make sense.)

It might make sense to direct feedback on the book to Wiley, but feedback on your post seems more suitable to direct to you. My feedback to you is not only that you ought not accept and propagate such a chart so uncritically, but also with regard to my point (2), that the sizes of the groups of silhouettes doesn’t correspond to average household sizes, contrary to your claim. I was able to spare myself $80 and look at a copy of the book, and I see that Farr does not make that claim anywhere; you added it. So you’re the one on the hook for that particular point.

As you say, one shouldn’t be too quick to infer intent. Ordinary non-malicious cockups in print tend to align with the author’s agenda as well for the simple reason that in copy-editing a book, the author is more likely to catch mistakes that seem wrong than ones that seem right. It would be lovely if one could check everything carefully, but having written (or co-authored) two books, I can report that this simply isn’t possible. Instead, one starts with the intuitive sense of implausibility as a guide for what to check more carefully. Where I do hold Farr responsible is for not having a well-publicized errata list with a way for readers to report additions that ought to be made to it. Back when I reviewed technical books, that was one of my criteria. Even an author who aspires to accuracy can’t get everything right, but they can and should put the mechanism in place for moving toward that goal after publication, once more eyes are on the book.

Technical publishers barely exist any more. They have just enough staff to hire freelancers on to do all the real work. It’s not just that they are prioritizing cost control over quality; it’s that there isn’t anyone left whose job could be quality.

Max, thanks for the excellent take down, that was well appreciated but I willing to give Bill some slack – I don’t imagine he gets paid a ton for posting at Streets MN, and this post wasn’t from some Facebook mean but a mainstream published book.

Also, Bill has had some decent analysis on some past charts posted, making some good critiques, see R. Florida…

Perhaps some charts like this can be posted as a discussion pt, with questions, as opposed to accepted fact.

I would also add to Max’s piling on the age distribution of the U.S. population has had some big ups and downs over decades – and so every aggregate, average type analysis should also factor in something we can compare. Like say, the sf per person of married couples empty nesters between age of 60-65 over past 50 years, or the sf person of single men and women between the ages of 30-40 over past 50 years etc, to avoid changes in averages simply due relative size of working age population, or elderly population at any given time.

And finally, does anyone know of someone that has done a better job of estimating this, change in SF person, SF per households and tracked say, something Max would approve of?

Sure, I appreciate very much the contributions Bill makes to our community and so I ought to cut him some slack. (As far as appreciating his contributions, by coincidence I saw your comment come in just after I linked to him as the expert on dive bars in the write-up I’m currently doing of the Holland neighborhood, where Jimmy’s et al are.) So, I appreciate your calling me out for using too harsh a tone. You are right. I was trying to hold him to a high standard as a sign that I had come to expect that of him, but I definitely went too far into grumpy. (This may well be a product of the flu-like symptoms I’m experiencing after a Shingrix vaccination, but that’s no excuse. I ought to know enough not to post when I’m grumpy. It could have waited.) The changing demographics are certainly complex. The whole idea of square footage per capita seems to imply that there ought to be a proportionality between people and area. But changing the number of people in a household doesn’t necessarily change how many square feet worth of kitchen you’d have, for example. So, although it makes sense as a measure of resource consumption (Farr’s point), it doesn’t necessarily make sense as something you would have any reason to expect to be the same—even at a given point in history—for different kinds of households. It would be great if someone were to do the work to unpack this all; I’m not volunteering.

No, I don’t get paid. The chart feature is something I do with spare time and the point is to generate conversation. This is a great example of a successful chart post IMO because Max has found many flaws.

Also, if anyone else wants to submit a Chart of the Day post, they don’t take very long. OR you can send me a chart you find intriguing with a few thoughts on why and I’ll put it up.

Thank you for posting these so frequently, Bill! I know it takes time to put them together, and you get paid precisely nothing to contribute your incredibly valuable insights. Thank you for starting conversations, and your generosity with your time.

Like, for example, posting the charts I sent yesterday and analyzing it so the world could understand what they had to say.

And anecdotally, at least in MSP, it seems the SF floor area per employee is way smaller than it used to be. Some office spaces that have way more people arriving by transit, walking, biking, still are having huge parking problems because there are so many more people in the same office spaces compared 20 years ago. So SF of commercial space would be interesting thing to look at also.